A369833 a(n) is the number of distinct values of the permanent of an n X n symmetric Toeplitz matrix using the first n prime numbers.
1, 1, 1, 6, 24, 120, 720, 5040, 40320, 362880
Offset: 0
Links
- Wikipedia, Toeplitz Matrix.
Programs
-
Mathematica
a[n_] := CountDistinct[Table[Permanent[ToeplitzMatrix[Part[Permutations[Prime[Range[n]]], i]]], {i, n !}]]; Join[{1}, Array[a,9]]
-
Python
from itertools import permutations from sympy import primerange, prime, Matrix def A369833(n): return len({Matrix([p[i:0:-1]+p[:n-i] for i in range(n)]).per() for p in permutations(primerange(prime(n)+1))}) if n else 1 # Chai Wah Wu, Feb 11 2024
Formula
a(n) <= A000142(n).
Conjectured e.g.f.: 1/(1 - x) - x^2/2.